Intensity correlation function, light scattering

In dynamic or quasi-elastic light scattering, a time dependent correlation function (i (0) i (t)) = G2 (t) is measured, where i (0) is the scattering intensity at the beginning of the experiment, and i (t) that at a certain time later. Under the conditions of dilute solution (independent fluctuation of different small volume elements), the intensity correlation function can be expressed in terms of the electric field correlation function gi (t)... 

Figure 2.5 Relaxation rates F of the intensity correlation functions as a function of q2 obtained via a photon correlation spectroscopy experiment. The sample was a w/o-droplet microemulsion made of D2 0/n-octane-di8/CioE4. On the oil-continuous side of the phase diagram the scattered light intensity is usually low leading to rather large errors of the individual data points. Nevertheless, from the slope of the linear fit the translational diffusion coefficient is obtained. (Figure redrawn with data from Ref. [67].)...

The dynamic behavior of linear charged polyelectrolytes in aqueous solution is not yet understood. The interpretation of dynamic light scattering (DLS) of aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) is particularly complicated. The intensity correlation function shows a bimodal shape with two characteristic decay rates, differing sometimes by two or three orders of magnitude, termed fast and slow modes. The hrst observations in low salt concentration or salt free solution were reported by Lin et al. [31] for aqueous solutions of poly(L-lysine). Their results are described in terms of an extraordinary-ordinary phase transition. An identical behavior was hrst observed by M. Drifford et al. in NaPSS [32], Extensive studies on this bimodal decay on NaPSS in salt-free solution, or solutions where the salt concentration is increased slowly, have been reported [33-36]. The fast mode has been attributed to different origins such as the coupled diffusion of polyions and counterions [34,37,38] or to cooperative fluctuations of polyelectrolyte network [33,39] in the semidilute solutions. 

The scattered light intensity correlation function C (/) has been measured over a very wide range of temperature and wave vectors for various systems. Typical intensity correlation functions C-(/) are depicted in Fig. 4 for the sake of illustration. These graphs show systematic deviations from the usual exponential decay, which are also observed for most of the systems we report in this part. As a remark, nonexponential decays that are small at low concentration, close to the critical point, become large for dense systems. From the initial slope of the time-dependent intensity correlation function, one can deduce the first cumulant F, which is the relaxation rate of the order parameter fluctuations. 

When monochromatic light is scattered by moving particles that show thermal motion, the field amplitudes E oo) show a Gaussian distribution. The experimental arrangement for measuring the homodyne spectrum is shown in Fig. 7.31. The power spectrum P (jo) of the photocurrent (7.68), which is related to the spectral distribution I oo), is measured either directly by an electronic spectrum analyzer, or with a correlator, which determines the Fourier transform of the autocorrelation function C(r) a i t)) i t -f- r)). According to (7.63), C(r) is related to the intensity correlation function G (r), which yields (7.64), and I co). 

The translational diffusion coefficient D of a polymer coil can be found from the time-dependent correlation function of scattered intensity measured in dynamic light-scattering experiments. Using the Stokes-Einstein equation, the translational diffusion coefficient D can be related to the apparent hydro-dynamic radius (the radius of equivalent hard sphere). In the limit of nondraining for the solvent coil formed by infinitely long chain, the hydrodynamic radius is given by... 

The principle of the measurement is illustrated in Figure 18.6. As particles diffuse due to thermal motion, the scattered light undergoes interference effects, and the scattered intensity fluctuates randomly with time. The information about particle size is contained in the rate of decay of the fluctuations, i.e. rapid diffusion of small particles leads to fast decay, while slow fluctuations result from the motions of larger particles. With modern correlator techniques, one can easily record the intensity correlation function /(r)/(0)) of the scattered light. This correlation function is written as follows ... 

Probe diffusion was determined using quasi-elastic light scattering spectroscopy. QELSS monitors the temporal evolution of concentration fluctuations by measuring the intensity I(q,t) of the light scattered at time t, and calculating the intensity-intensity correlation function... 

How are light scattering spectra related to the mohons of scattering centers in soluhon In a QELSS experiment, one illuminates the sample of interest with abeam of coherent monochromahc light, and uses signal analysis methods to characterize fluctuations in the hme-dependent intensity I q,r) of the scattered light. QELSS measures directly the intensity—intensity correlation function or dynamic structure factor S q,t) ... 

The correlator (6) is of the utmost importance because its generating function enters into an expression which describes the angular dependence of intensity of scattering of light or neutrons [3]. It is natural to extend expression (6) for the two-point chemical correlation function by introducing the w-point correlator ya1... (kl...,kn l) which equals the joint probability of finding in a macromolecule n monomeric units Maj.Ma> divided by (n-1) arbitrary sequences... 

This effective Q,t-range overlaps with that of DLS. DLS measures the dynamics of density or concentration fluctuations by autocorrelation of the scattered laser light intensity in time. The intensity fluctuations result from a change of the random interference pattern (speckle) from a small observation volume. The size of the observation volume and the width of the detector opening determine the contrast factor C of the fluctuations (coherence factor). The normalized intensity autocorrelation function g Q,t) relates to the field amplitude correlation function g (Q,t) in a simple way g t)=l+C g t) if Gaussian statistics holds [30]. g Q,t) represents the correlation function of the fluctuat-... 

With the availability of lasers, Brillouin scattering can now be used more confidently to study electron-phonon interactions and to probe the energy, damping and relative weight of the various hydro-dynamic collective modes in anharmonic insulating crystals.The connection between the intensity and spectral distribution of scattered light and the nuclear displacement-displacement correlation function has been extensively discussed by Griffin 236). 

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